Current codes incorporate simplified methods for the prediction of acceleration demands on secondary structural and non-structural elements at different levels of a building. While the use of simple analysis methods should be advocated, damage to both secondary structural and non-structural elements in recent earthquakes have highlighted the need for improved design procedures for such elements. In order to take a step towards the formation of accurate but simplified methods of predicting floor spectra, this work examines the floor spectra on elastic and inelastic single-degree of freedom systems subject to accelerograms of varying seismic intensity. After identifying the factors that appear to affect the shape and intensity of acceleration demands on secondary structural and non-structural elements, a new series of calibrated equations are proposed to predict floor spectra on single degree of freedom supporting structures. The approach uses concepts of dynamics and inelasticity to define the shape and intensity of the floor spectra at different levels of damping. The results of non-linear time-history analyses of a series of single-degree of freedom supporting structures indicate that the new methodology is very promising. Future research will aim to extend the methodology to multi-degree of freedom supporting structures and run additional verification studies.